Mr Martin is also expected to tell Mr Kenny that Fianna Fáil will not facilitate a Fine Gael government if he does not win the support of at least eight Independent TDs. Fianna Fáil needs Fine Gael and Independents to have a combined 58 seats in a future government to allow Mr Martin's party abstain from certain votes.

For the first time in weeks, Mr Martin yesterday dug his heels in on the issue of water charges after he abandoned his plans to become the Taoiseach.

Fianna Fáil last night conceded that the next government is likely to be a Fine Gael-led minority administration after Mr Martin's ultimatum to Independents backfired.

Mr Martin picked up no additional votes - in contrast to Mr Kenny who received a boost after securing the support of Dublin South West TD Katherine Zappone.

The two party leaders were scheduled to meet last night to discuss how to get talks aimed at forming a minority government back on track.

But in a significant development, Mr Martin was instructed by his own TDs to refuse to put any deal on a minority government in writing.

At the Fianna Fáil parliamentary party meeting, backbenchers pointed to the 'Tallaght Strategy' - an agreement struck in 1987 which worked on a case-by-case basis.

But a senior Fine Gael negotiator told the Irish Independent the party is pushing for guarantees for support for a period of at least three years.

The issue is likely to come to a head when the two teams reconvene. The same source admitted the gap between the two parties on water could "make or break" negotiations.

After yesterday's vote, Mr Martin accused Fine Gael of acting in an "unhelpful and provocative" manner after the party passed a motion this week reaffirming its commitment to a national utility.

Despite admitting that the future of water is "not the single most important issue facing our country", Mr Martin indicated that his party's desire to suspend charges remains.

And he demanded an investigation into the money spent by Irish Water on a "post-election lobbying campaign" designed to prevent its abolition.

Fine Gael wants to maintain charges and the public utility - while Fianna Fail is adamant charges must be suspended and Irish Water replaced with a slimmed-down body.

As expected, yesterday's vote for Taoiseach - proved inconclusive. Mr Kenny did secure the support of Ms Zappone as 14 other Independent TDs opted to abstain from the vote and withdraw from the talks.

In a further boost for Mr Kenny, there were indications last night that Labour is moving to support the Fine Gael leader at a future vote for Taoiseach.

A source said if Fine Gael agreed to certain demands "important to us a party", Labour's seven TDs may lend their support to Mr Kenny.

"We have a policy platform that we want implemented. We will discuss our next move but everything is on the table," said the source.

After the vote, Mr Kenny extended an invitation to Mr Martin to reopen talks between the two main parties on forming a government - just hours after talks between the two parties' negotiation teams broke down.

Mr Martin addressed his own TDs on two occasions yesterday as questions were raised internally over his decision to issue the ultimatum to Independents.

Fianna Fail negotiator Charlie McConalogue admitted last night Mr Martin's defeat meant the party is giving up on leading a minority government.

The Irish Independent has learned that a claim by Fine Gael during the negotiations - that the party was on the cusp of securing the support of six Independents - prompted Mr Martin's gamble.

A senior Fianna Fail source said the claim "contradicted strongly" what Mr Martin was being told privately by Independents about their voting intentions.